Theorem xornan 1472

Description: XOR implies NAND. (Contributed by BJ, 19-Apr-2019.)

Assertion

Ref	Expression
xornan	|- ( ( ph \/_ ps ) -> -. ( ph /\ ps ) )

Proof of Theorem xornan

Step	Hyp	Ref	Expression
1		xor2 1470	. 2 |- ( ( ph \/_ ps ) <-> ( ( ph \/ ps ) /\ -. ( ph /\ ps ) ) )
2	1	simprbi 480	1 |- ( ( ph \/_ ps ) -> -. ( ph /\ ps ) )

Syntax hints:   -. wn 3   -> wi 4   \/ wo 383   /\ wa 384   \/_ wxo 1464

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-xor 1465

This theorem is referenced by:  xornan2  1473  mptxor  1694